Head on collision

Two spheres X and Y (no mentioning about them being identical in mass but drawn in equal sizes) are about to collide head on. Their initial velocities are +5ms^-1 and -5ms^-1 initially, moving towards each other with X being towards east. Assuming completely elastic and head-on collision, what happens to the spheres after collision?

The answer I was given was that X comes to a rest while Y moves off in the reverse direction, that is, east with 10ms^-1.

Why is this so? I don't really understand why is it that Y would move off and not the other way around where X moves off towards west with 10ms^-1? Why is all momentum transfered to Y and not X? I apologise that I don't have any workings with me when I should have but I'm confused with the principles here. Also, does the relative speed of approach only applicable to elestic collisions?

Two spheres X and Y (no mentioning about them being identical in mass but drawn in equal sizes) are about to collide head on. Their initial velocities are +5ms^-1 and -5ms^-1 initially, moving towards each other with X being towards east. Assuming completely elastic and head-on collision, what happens to the spheres after collision?

The answer I was given was that X comes to a rest while Y moves off in the reverse direction, that is, east with 10ms^-1.

The answer you were given is obviously wrong, if the masses are the same. Conservation of momentum requires that the centre of mass does not change. The centre of mass is at rest in the lab frame. They both recoil at 5 m/sec in opposite directions.

Yes, as AM said the answer is definitely wrong .
Imagine this, there is nothing special given about mass X or Y . That is the names can be used interchangeably(except for the direction of velocity), this implies that whatever causes an effect on both objects simultaneously (like a collission) should show symmetrical effects. So the answer is clearly wrong ( As you have observed, why isn't it the other way round ?).
The only way to distinguish further between X and Y is to give their masses and they are not the same too.

The masses will definitely not come to rest, if the collission is elastic (why ?).
If you could give us all the options in the MCQ , we could direct you to the right answer, perhaps it involves eliminating all other options, since the masses are not given .